Apparatus for microinductive investigation of earth formations

ABSTRACT

A wall-engaging apparatus for microinductively investigating a characteristic of an earth formation traversed by a borehole includes an antenna set mounted in a sensing body adapted for sliding engagement with the wall of the borehole. The antenna set includes first, second and third antenna elements. The second and third elements, being structurally identical but differentially coupled, are positioned in electromagnetic symmetry about the first antenna element. Either the first antenna element or the differentially coupled second and third antenna elements may be energized by suitable circuits, while the other is coupled to circuits for receiving signals indicative of a set characteristic. In another wall-engaging apparatus for microinductively investigating a characteristic of earth formations traversed by a borehole, a transmitter antenna is mounted in a conductive wall-engaging body, within a volume bounded in part by an integral conductive backplane and conductive side wall and opening to the wall-engaging face of the body, for coupling focused electromagnetic energy into a formation. The volume preferably is conformal with the transmitter antenna. Circuits are provided for energizing the transmitter antenna and for detecting a magnetic field from the engaged formation arising from the coupled electromagnetic energy.

BACKGROUND

The present invention relates to methods and apparatus for highresolution measurement of one or more characteristics of earthformations traversed by a borehole, and more particularly to methods andapparatus for high resolution measurement of one or more characteristicsof earth formations traversed by a borehole for determining the dip andazimuth of these formation beds.

One of the most valuable aids in the exploration for oil and gas is thedipmeter log, which provides positive structural and statigraphicinformation for both exploration and development drilling programs.Advances in dipmeter tool design, magnetic taping, machinecomputerization, and interpretation methods make it possible torecognize such features as structural dip, faults, unconformities, bars,channels, and reefs. In addition, the direction of sedimentation and ofpinchouts can be estimated. When combined with the data from otherwells, dipmeter information helps to establish the overall structuraland stratigraphic picture of the area under study.

The focussed current type of dipmeter has been particularly wellreceived by the wireline logging industry for use in logging boreholesdrilled with conductive drilling fluids. Focussed current dipmeter toolsemploy at least three pads and commonly four, each of which comprisesone or more electrodes for emitting a focussed current beam into theadjacent formation. The current flow at each electrode is proportionalto the conductivity of the adjacent formation. Focussed currentdipmeters are described in U.S. Pat. No. 3,060,373, issued Oct. 23, 1962to Doll; U.S. Pat. No. 4,251,773, issued Feb. 17, 1981 to Cailliau etal; and U.S. Pat. No. 4,334,271, issued June 8, 1982 to Clavier. Theseare able to achieve good vertical resolution at resonable loggingspeeds, the micro-resistivity sensors used on some of these tools beingcapable of resolution to as fine as 0.2 inch.

The great amount of data acquired by dipmeters, and especially the highresolution focussed current dipmeters, is advantageously exploited bythe use of computers. For example, suitable computer implementedcorrelation techniques are described in U.S. Pat. No. 4,348,748, issuedSept. 7, 1982 to Clavier et al., and U.S. Pat. No. 4,335,357, issuedOct. 19, 1982 to Chan. Improved dip determinations often can be obtainedby use of other computer-implemented techniques, such as that describedin U.S. Pat. No. 4,453,219, issued June 5, 1984 to Clavier et al.

Other types of dipmeters have been proposed for use in boreholes drilledwith conductive drilling fluids, including the electrical-toroidal typedescribed in U.S. Pat. No. 2,987,668, issued June 6, 1961 to Gondouin.None of them has achieved the popularity of the focussed current tools.

Unfortunately, electrical dipmeters, including the focussed currenttype, are not altogether satisfactory for use in boreholes which havebeen drilled with a nonconductive fluid such as air or an oil-based mud.Electrical dipmeters require a conductive medium to permit the flow ofcurrent from the electrode system into the formation. This conductivemedium is not present in boreholes drilled with air or an oil based mud.

Various approaches employing pad-mounted electrodes have been taken toobtain dip information in wells drilled with nonconductive drillingfluids. One approach, which is exemplified by U.S. Pat. No. 2,749,503,issued June 5, 1956 to Doll, and more recently by U.S. Pat. No.3,973,181, issued Aug. 3, 1976 to Calvert, uses high frequencyelectromagnetic energy to measure the capacitive coupling of anelectrode to the formation. Another approach, described in an article byFons entitled "New Dipmeter Tool Logs in Nonconductive Mud," The Oil andGas Journal, Aug. 1, 1966, pp. 124-26, advocates the use ofmonoelectrode contact knife-like electrodes to make direct contact withthe formation.

Other approaches to obtain dip information in wells drilled withnonconductive drilling fluids dispense with electrodes altogether.Acoustic techniques employing pad-mounted acoustic transducers aretaught in, for example, U.S. Pat. No. 3,376,950, issued Apr. 9, 1968 toGrine; U.S. Pat. No. 3,526,874, issued Sept. 1, 1970 to Schwartz; andU.S. Pat. No. 3,564,914, issued Feb. 23, 1971 to Desai et al. Anelectromagnetic wave logging dipmeter is disclosed in U.S. Pat. No.4,422,043, issued Dec. 20, 1983 to Meador.

In addition, techniques based on the principal of induction logging havebeen proposed for measuring dip by the use of either mandrel-mountedcoils or pad-mounted coils. In conventional induction logging, such asdisclosed in U.S. Pat. No. 2,582,314, issued Jan. 15, 1952 to Doll,oscillating magnetic fields formed by one or more energized inductioncoils induce currents in the formation around the borehole. Thesecurrents in turn contribute to a voltage induced in one or more receivercoils through a secondary magnetic field. The voltage component of thereceived signal that is in phase with respect to the transmittercurrent, known as the R-signal, is approximately proportional toformation conductivity.

When operating a mandrel tool in a borehole traversing a homogeneousmedium, ground current flow loops arise which coincide with the primaryelectric field induced by the primary magnetic field of the transmitter.Hence, the ground loops are coaxial relative to the receiving andtransmitting coils and the borehole. Under certain conditions of thesurrounding earth formations, however, such as dipping beds orfractures, the average plane of the ground current flow loops vary fromthis coincident alignment. The phenomena is exploited in themandrel-type induction dipmeter. In one early mandrel inductiondipmeter, a coil array is mechanically rotated to produce modulationcomponents in the receiver signals at the frequency of rotation of thecoil array. The modulation components are processed to obtainindications of the dip, dip azimuth and/or anisotrophy. More recently,techniques have been proposed which utilize mechanically passiveinduction coil arrays to obtain measurements of formation dip, dipazimuth, and/or anisotropy. Systems of this type are taught in, forexample, U.S. Pat. No. 3,808,520, issued Apr. 30, 1974 to Runge; U.S.Pat. No. 4,302,723, issued Nov. 24, 1981 to Moran; and U.S. Pat. No.4,360,777, issued Nov. 23, 1982 to Segesman.

Other induction techniques use pad-mounted field generating and sensingtransducers to measure such characteristics are conductivity, magneticsusceptibility, and dielectric constant, as well as the dip of earthformations. An early system is described in U.S. Pat. No. 3,388,323,issued June 11, 1968 to Stripling. The stripling apparatus comprisesthree circumferentially spaced sensors which are urged against theborehole wall. A composite field comprising a primary magnetic field anda secondary magnetic field is created and sensed by each sensor. Phaseseparation is applied to the sensed signal to obtain measurements ofmagnetic susceptibility and electrical conductivity. The sensor of theStripling apparatus comprises a coil wrapped around a core ofhigh-permeability material to increase the flow of magnetic flux throughthe coil. The coils have a length of about three inches and a diameterof about one-half inch. The axes of the coils are tangential to a circlelying in a plane normal to the tool axis. Separate transmitting andreceiving coils are contemplated as well. The apparatus operates atfrequencies under 60 kHz.

A pad configuration intended to reduce sensitivity to borehole diameterand borehole fluid conductivity is disclosed in U.S. Pat. No. 3,539,911,issued Nov. 10, 1970 to Youmans. The pad comprises a pair of transmittercoils, said to be wound in series opposition, mounted within the pad atan acute angle from the longitudinal axis of the elongated sonde, and areceiver coil mounted substantially parallel to the longitudinal axisbetween the transmitter coils. The mounting angles of the transmittercoils are chosen to provide what is said to be a desired asymmetricalfield of investigation. The apparatus operates at about 20 kHz, and bothin-phase or out-of-phase detection techniques are contemplated. Theaxial distance between the axes of the transmitter and receiver coilsare said to influence the investigative mode, and mutual balance of thecoil configuration is said to be attained by adjusting that distance.

More recently, U.S. Pat. No. 4,019,126, issued Apr. 19, 1977 to Meadordisclosed an apparatus intended to avoid the temperature and pressuresensitivity of the aforementioned Stripling apparatus. Meador teachesthat the sensing coil of an induction dipmeter arm may be constructedwithout a high permeability core, which is quite temperature andpressure sensitive. The coil proposed by Meador comprises two turns ofone-eighth inch diameter copper wire, each turn being approximatelythree-quarters of an inch by three-eighths of an inch. Meador alsoteaches that two separate coils may be employed in each pad, one coilbeing the transmitter and the other being the receiver. The coil isarranged with its longitudinal axis parallel to the axis of the sonde.The coil is coupled with a capacitor to form a tank circuit, which isconnected to an oscillator circuit. The operating frequency is said tobe in the range of preferably between 50 MHz and 200 MHz, withsatisfactory operation at lower frequencies as well. The Meadorapparatus is intended to measure resistivity and dielectric constant.

The pad-mounted induction dipmeter systems generally have beendisappointing. Some of the techniques are sensitive to borehole diameterand fluid conductivity, or to borehole temperature and pressure.Moreover, some of the systems themselves are not highly sensitive to thevery parameters they are intended to measure, which is particularlytroublesome when effects resulting from temperature, pressure, alignmentinaccuracies, and operation instabilities, contribute to the detectedsignal.

SUMMARY OF THE INVENTION

An object of the present invention, therefore, is to provide a novelsensor suitable for microinductively determining one or morecharacteristics of an earth formation, such as conductivity, dielectricconstant, and/or the dip and azimuth of earth formation bedding.

Another object of the present invention is to provide a microinductionsensor that is suitable for use in a borehole drilled with anonconductive drilling fluid.

Yet another object of the present invention is to provide amicroinduction sensor that performs well under various borehole pressureand temperature conditions.

These and other objects are achieved by a wall-engaging apparatus formicroinductively investigating a characteristic of earth formationstraversed by a borehole, in accordance with the present invention. Theapparatus comprises an antenna set mounted in a longitudinally elongatedbody. The elongated body is adapted for a sliding engagement with thewall of the borehole. The antenna set includes a first antenna elementand identical second and third antenna elements, the respectivelocations and orientations of the second and third antenna elementsbeing selected to place the second and third antenna elements inelectromagnetic symmetry about the first antenna element. Means areincluded for differentially coupling said second and third antennaelements. Either the first antenna element or the differentially-coupledsecond and third antenna elements may be energized by suitable meanswithin a frequency range of 1 MHz and 300 MHz to couple electromagneticenergy into a formation being investigated, while the other is coupledto means for receiving signals indicative of the characteristic. Severalembodiments are described.

These and other objects also are achieved by a well-engaging apparatusfor microinductively investigating a characteristic of earth formationstraversed by a borehole that comprises a longitudinally elongatedconductive body adapted for a sliding engagement with the wall of theborehole, and a transmitter antenna mounted in a metal body within avolume bounded in part by an integral conductive backplane andconductive sidewall and opening to the wall-engaging face of the bodyfor coupling focussed electromagnetic energy into a formation engaged bythe well-engaging face of the body. The volume preferably is conformalwith the transmitter antenna. Means are included for energizing thetransmitter antenna and for detecting a magnetic field from the engagedformation arising from the coupled electromagnetic energy.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, where like reference characters indicate like parts:

FIG. 1 is an illustration useful in explaining theory of operation;

FIG. 2 is a plan view of a borehole logging tool;

FIG. 3 is a plan view of a transmitter loop;

FIG. 4 is a plan view of a receiver loop;

FIG. 5 is a plan view of an electroquasistatic shield;

FIG. 6 is a perspective view of an assembled antenna set;

FIG. 7 is a cross-sectional view of a logging pad;

FIG. 8 is a schematic view of an electronic circuit;

FIGS. 9, 10, 11 and 12 are graphs useful in explaining device response;

FIG. 13 is a cross-sectional view of another antenna set;

FIG. 14 is an illustration useful in explaining theory of operation;

FIG. 15 is a graph useful in explaining device response;

FIG. 16 is a simplified perspective view of a sensor with backplaneelement;

FIG. 17 is a cross-sectional view of another logging pad; and

FIGS. 18 and 19 are illustrations useful in explaining theory ofoperation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention may be better understood in the context of theunderlying principle of one of the embodiments, explained with referenceto the simplified representation of FIG. 1. A sensor 7 includes atransmitter loop 10 and two receiver loops 12 and 14 nominallypositioned symmetrically about and coaxial with the transmitter loop 10.The transmitter loop 10 is coupled to a source of oscillatory current16. Receiver loops 12 and 14 are connected in series opposition to areceiver 18. The sensor 7 is positioned in the borehole 30 such that theplanes of the transmitter loop 10 and receiver loops 12 and 14 areparallel to a plane tangential to the borehole wall to a location whereformation 36 is to be investigated. The oscillating current flowing inthe transmitter loop 10 creates a primary magnetic field B_(p),exemplary field lines of which are shown in FIG. 1. A primary electricfield (not shown) is induced by the primary magnetic field B_(p). Theprimary electric field causes oscillating currents, termed eddycurrents, to flow in nearby conductive material. Eddy currents flow inclosed loops which in a homogeneous material are coaxial with thetransmitter loop 10. An exemplary eddy current unit ground loop isrepresented at 20. Since these eddy currents do not cross the boundarybetween the borehole 30 and surrounding formation, the presence of aninsulating mud or mudcake does not interrupt the individual currentpaths in the formation. The magnitude of these eddy currents isproportional to the current in the transmitter loop 10 and theconductivity of the formation, and create a relatively weak, secondarymagnetic field B_(s), exemplary field lines of which are illustrated inFIG. 1, that is detected by the receiver loops 12 and 14.

Normally, the detection of the secondary magnetic field B_(s) is quitedifficult due to the presence of the considerably stronger primarymagnetic field B_(p). To overcome this problem, the receiver loops 12and 14 are placed symmetrically about and coaxial with the transmitterloop 10, and are wired in series opposition. In this arrangement, theflux of the primary magnetic field B_(p) passing through the receiverloops 12 and 14 is identical; hence their responses to the primarymagnetic field B_(p) cancel. As is apparent from FIG. 1, the flux of thesecondary magnetic field B_(s) passing through the receiver loop 12 isstronger (i.e., lines of flux more closely spaced) than the flux passingthrough the receiver loop 14. Hence, a voltage V_(l) arises from thecurrent induced in the receiver loops 12 and 14 by the secondarymagnetic field. The voltage V_(l) is proportional to the conductivity ofthe formation.

A better appreciation of the theoretical basis of this embodiment may behad by describing the response of sensor 7 with the geometrical factortheory, a quasi-static approximation first used by Henri Georges Doll todescribe induction logging tools. In accordance with a low frequencyapproximation, the electric field generated by an electric current loopof radius ρ' located at z' is, assuming e^(-i)ωt dependence ##EQU1##where (ρ,z) is the observation point, and where F(k) and E(k) areelliptical integrals. A normalized electric field E.sub.φ is defined as

    E.sub.φ =iωμIρ'E.sub.φ                (3)

In the presence of a conductive medium, a current loop at (a,0), such asthat supported by the transmitter loop 10, induces an eddy currentground loop, such as indicated at 20, given by

    J.sub.φ (ρ',z')=iωμσIaE.sub.100 (ρ',z';a,0) (4)

This ground loop produces a secondary electric field given by

    ΔE.sub.φs (ρ,z)=iωμJ.sub.φ (ρ',z')Δρ'Δz'ρ'E.sub.φ (ρ,z;ρ',z')=-ω.sup.2 μ.sup.2 σIaΔρ'Δz'ρ'E.sub.φ (ρ,z;a,0)E.sub.φ (ρ,z;ρ',z')                                       (5)

which in turn induces a voltage across the receivers 12 and 14, wired inseries opposition. This voltage is

    ΔV=-2π[b.sub.1 ΔE.sub.φs (b.sub.1,h.sub.1)-b.sub.2 ΔE.sub.φs (b.sub.2,-h.sub.2)]=2πω.sup.2 μ.sup.2 σIaρ'Δρ'Δz'E.sub.φ (ρ',z';a,0)[b.sub.1 E.sub.φ (b.sub.1,h.sub.1 ;ρ',z')-b.sub.2 E.sub.φ (b.sub.2,-h.sub.2 ;ρ',z')]                            (6)

In the above (b₁,h₁) and (b₂,-h₂) are the receiver locations. They arechosen so that the direct mutual coupling between the transmitter andthe receivers is zero. In the absence of a ground plane, nominally b₁=b₂ and h₁ =h₂.

The total voltage across the receiver loops 12 and 14 due to all groundloops in the formation is ##EQU2## where G(ρ',z'), which is ageometrical factor that denotes where the signal is coming from in theformation, may be expressed as

    G(ρ',z')=ρ'E.sub.φ (ρ',z',a,0)[b.sub.1 E.sub.φ (b.sub.1,h.sub.1 ;ρ',z')-b.sub.2 E.sub.φ (b.sub.2,-h.sub.2 ;ρ',z')]                                              (8)

It has been found that the geometrical factor is peaked around ρ=L_(e)where L_(e) is a length that depends on the dimensions of the antennaarray and the distance from the sensor. Since the geometrical factor issymmetric about ρ=0, the part of the formation that contributes most tothe signal has the shape of a truncated cone.

A normalized geometrical factor, which is a function of antenna standofffrom the borehole wall, can be expressed as ##EQU3## The apparentconductivity then is given by: ##EQU4## where G(ρ',z') and G(ρ',z') arerelated as:

    G(ρ',z')=cG(ρ',z')                                 (11)

and where ##EQU5## This relates the voltage at the receivers to theconductivity of the formation.

It is to be noted that the voltage across the receiver loops 12 and 14due to the formation signal given by Equation (7) is proportional to ω²μ². The primary voltage at the receiver loops 12 and 14, which is thedirect mutual coupling, is proportional, if not canceled, to theelectric field given by Equation (1), i.e. is proportional to iωμ. Whilethe direct mutual coupling is cancelled by the symmetrical arrangementof sensor 7, the stability of the cancellation does depend on the ratioof the formation signal to the direct mutual coupling signal. The ratioof the formation signal to the primary signal is approximately iωμσL_(e)where L_(e) is an effective length determined by antenna arrayparameters. Hence, the sensor preferably should be operated at a highfrequency to improve stability. The resolution of the coil set isapproximately L_(e), while the depth of investigation is also of theorder of L_(e).

The geometrical factor theory is a quasistatic approximation and doesnot work very well unless ωμσL_(e) ² is much less than 1. This isbecause the skin and propagation effects are ignored. For manyfrequencies of interest, however, the geometric factor theory is quiteadequate.

The problem of a current loop radiating above a transversely isotropicstratified medium can be solved exactly incorporating all wave effects.The electric field due to a current loop indicated at (ρ',z') is##EQU6## where R^(TE) is the fresnal reflection coefficient for ahorizontally stratified medium, where the stratified medium starts atz=d_(o). In the presence of a ground plane, the electric field can bemodified as follows: ##EQU7##

While many of the novel features of the present invention are generallyuseful in making borehole measurements, the present invention isparticularly advantageous for use in investigating structural andstratigraphic dip, especially in boreholes drilled with nonconductivefluids. A "dipmeter" tool in accordance with the present invention isshown generally at 51 in FIG. 2, residing in a borehole 30. The borehole30, possibly drilled using a nonconductive drilling fluid such as anoil-based mud, traverses typical earth formations represented by shaleformations 32 and 36 and an intervening sand formation 34, whichincludes sand beds 42 and 46 with shale layers such as 44. A typicalstructural boundary is represented by boundary 38 between earthformations 32 and 34 and boundary 40 between earth formations 34 and 36.A typical stratigraphic boundary is represented by boundary 48 andboundary 50. Moreover, sand formations 42 and 46 may comprise variousstrata of sand (not shown) having different characteristics, such ascoarse and fine grains. Other stratigraphic features may be present aswell. The tool 51 comprises an elongated central support member 52adapted for movement through the borehole 30. The elongated member 52supports four substantially identical pads 54(1), 54(2), 54(3), and54(4) (hidden), which are urged against the wall of the borehole 30 byrespective arm mechanisms 56(1), 56(2), 56(3) and 56(4) hidden inassociation with collar 60. Collar 60 is mounted on the elongatedsupport member 62, and slides on the member 52 to allow for expansionand contraction of the arm mechanisms 56(1)-56(4). The tool 51 alsoincludes a suitable centering guide assembly coupled to the upper end ofthe elongated support member 52. The centering guide assembly includesflexible spring arms 62(1), 62(2), 62(3) and 62(4) (hidden), which areconnected to suitable collars 64 and 66. One of the collars 64 and 66 issecured to the support member 52. The other collar is mounted on thesupport member 52, and slides on the member 52 to allow for expansionand contraction of the spring arms 62(1)-62(4). The centering guideassembly comprising springs 62(1)-62(4) cooperates with pads 54(1)-54(4)and associated arm mechanisms 56(1)-56(4) to maintain the tool 51centered in the borehole 30.

The tool 51 is connected at its upper end to an armored multiconductorcable 68 to surface apparatus. The surface apparatus includes a sheave11 over which the multiconductor cable 68 passes to a suitable drum andwinch mechanism 13, for raising and lowering tool 51 through borehole30. Electrical connection between the cable 68 and telemetry, controland power circuits 17 is made through a suitable multielement slip ringand brush contact assembly (not shown) and cable 15. The depth of thetool is determined by the use of a suitable measuring wheel mechanism19, which is also connected to the telemetry, control and power circuits17 by cable 21. Other surface instrumentation includes a processor 25connected to the telemetry, control and power circuits 17, and operatorterminal and input/output devices 27 connected to the processor 25.

The pads 54 may be as shown at 120 in FIG. 7, as shown at 400 in FIG.17, or as otherwise described below. An understanding of theseembodiments will be facilitated by the following description of alaboratory implementation of an antenna set for which the transmitterloop 10, the receiver loops 12 and 14, and individual shield elementswere fabricated from photolithographic masks with printed circuit boardtechnology. The printed circuit boards were constructed of one ouncecopper cladded polyimide material. A thin deposit of gold was platedonto the copper to control oxidation. The board material was 1.5 mmthick and reasonably rigid.

The transmitter loop 10 is illustrated in FIG. 3. The flat copper loopmeasures 2.0 cm in diameter and is broken at the point where terminalleads 72 and 74 are provided. The receiver loop 12 is illustrated inFIG. 4. The flat cooper loop measures 1.0 cm in diameter and is brokenat the point where terminal leads 76 and 78 are provided. Receiver loop14 is identical to receiver loop 12. The transmitter loop 10 and thereceiver loops 12 and 14 were characterized between 10 MHz and 50 MHz.The transmitter loop 10 was found to have an inductance of 88 nH and aseries resistance of 0.3Ω. The receiver loops 12 and 14 were found tohave an inductance of 63 nH and a series resistance of 0.6Ω. Theresonant frequencies of these devices were several hundred MHz. It willbe appreciated that the size of the loops 10, 12 and 14 controls themagnitude of the output signal, the volume of rock formationinvestigated (spatial resolution), and the depth of investigation.Generally, these factors increase with increasing loop size.

The laboratory sensor was formed by assembling the individual printedcircuit boards upon which the transmitter loop 10 and receiver loops 12and 14 had been fabricated. Receiver loops 12 and 14 were arranged in"electromagnetic symmetry" about the transmitter loop 10. Generally,electromagnetic symmetry is defined as M_(ac) =M_(bc), in which therelative location and orientation, and the antenna parameters, ofantennae A, B and C are such that the mutual induction between antennaeC and A is used to cancel the mutual induction between antennae C and B.Electromagnetic symmetry is achieved in the present embodiment, forexample, by physically locating the receiver loops 12 and 14 coaxiallywith and symmetrically about the transmitter loop 10. A suitabletransmitter-receiver loop spacing was found to be 0.69 cm, althoughcloser spacing is possible if some loss of sensitivity can be tolerated.

Electroquasistatic coupling was found to be present between the variousloop antennas and between the antenna set and the formation. Thiselectroquasistatic coupling can be tolerated in many instances, althoughit may be eliminated where desired by the use of shield elements. Asuitable shield element is shown at 80 in FIG. 5. The shield 80comprises a number of conductive segments, for example 256 as indicatedat 110(1), 110(2), . . . , 110(256), radiating from a conductive center.The shield element 80 is radially slit to avoid the generation ofazimuthal eddy currents therein by the azimuthal electric field inducedby the magnetic fields. It will be noted that the etched lines of theshield image 80 extend to the edge of the metallic cladding. Moreover,the 256 etched lines are very closely spaced, insuring that distrubanceof the magnetic field is minimized. Common electrical connection isprovided only at this conductive center, which confers more completeshielding and a free path for radial currents. The shield 80 is squareand measures 10 cm on a side. A shield terminal lead 82 is provided.

A reduction in the sensitivity of the laboratory sensor to resonantcoupling of the transmitter loop 10 to the receiver loops 12 and 14, andof the antenna array to the formation was achieved by placing individualshield elements preferably between the transmitter loop 10 and each ofthe receiver loops 12 and 14, and between each of the receiver loops 12and 14 and the external environment. Individual shield elements 80 wereplaced symmetrically about and coaxial with the transmitter loop 10 at adistance of 1.5 mm, the thickness of a printed circuit board. Individualshield elements 80 also were placed symmetrically about the outside ofand coaxial with the receiver loops 12 and 14, also at a distance of 1.5mm. The overall thickness of the fully assembled laboratory sensor,including shield elements and a protective outer layer of circuit boardmaterial, was 2.0 cm. Moreover, undesirable resonances, which would haveincreased the sensitivity of the sensor to variations in ambientconditions, were eliminated in the laboratory antenna set when shieldssuch as 80 were included.

A more practical implementation of a sensor is shown generally at 70 inFIG. 7. The sensor 70, which provides an absolute measurement offormation conductivity, comprises an antenna set 69 which preferably hasbeen metalized on the sidewall and back. The sensor 70 is set in acircular cavity centered in the metal body 122 of the exemplary pad 120and fixed therein by a suitable adhesive. The rearward metalized portion26 forms a highly conductive backplane which functions to isolate theantenna set 69 from sonde and borehole effects as explained below.Moreover, the backplane 126 and conductive sidewall metalized portion127 cooperate to improve the focussing of the various magnetic fields,as explained below. The metalization of the antenna set 69 may beomitted, in which instance the functions of the backplane 126 andsidewall 127 will be provided by the cavity itself. While suchimprovements in focussing and isolation are quite advantageous, they arenot necessary in providing a functional sensor.

The antenna set 69 of FIG. 7, shown in more detail FIG. 6, comprises thetransmitter loop 10, the receiver loops 12 and 14, and if desiredsuitable electroquasistatic shield elements, arranged essentially asdescribed above with respect to the laboratory implementation of thesensor but for a change necessitated by the use of the backplane 126.Other notable differences include the use of sidewalls about the antennaset 69 for improving the focussing of the composite magnetic field, themethod of assembling the various elements of the sensor 70, and theimplementation of one of the shield elements. Also, it may be desirablein some instances to use a thicker copper film in fabricating thetransmitter loop 10 to avoid excessive joule heating. It will beunderstood that the dimensions given herein are illustrative only, andthat other dimensions may be quite satisfactory as well.

The backplane 126 is a conductive sheet which isolates the antenna set69 from the effect of conductive substances in the borehole 30 andexerts a predictable, hence correctable effect on the antenna set 69.Avoidance of conductive substances, even in a borehole drilled with anonconductive drilling fluid, is unreliable in practice, particularly asthe arm mechanisms 56 and the tool support member 52 are metallic. Thebackplane 126 acts much like a mirror with respect to radio frequencymagnetic field. The spatial resolution of the an embodiment withbackplane is unchanged and the depth of investigation decreased onlyvery slightly from an embodiment without backplane. In theory, a currentloop in the presence of a ground plane generates an electric field givenby

    E.sub.φp =-jωμIρ'[E.sub.φ (ρ,z;ρ',z')-E.sub.φ (ρ,z;ρ',-z'+2d)]  (16)

where E.sub.φ is defined in Equation (3). The image theorem was invokedin the above. The analysis follows as before.

A suitable location for the backplane 126 has been found to be about 1.0cm behind the receiver loop 14, although this distance is not criticaland a lesser distance may be used if a thinner sensor is desired. Tocompensate for the difference in flux coupled into the receiver loops 12and 14 by the image current attributable to the backplane 126, one ofthe the receiver loops 12 and 14 must be displaced from exact physicalsymmetry to maintain electromagnetic symmetry. In the antenna set 69 ofpad 120, the receiver loop 14 is moved about 0.08 mm closer to thetransmitter loop 10.

The conductive cylindrical sidewall 127 about the antenna set 69 has twomajor effects, one quite advantageous and the other quite troublesome.On the one hand, the cylindrical sidewall 127 significantly enhances theresolution of the sensor 70, hence improving its thin bed response. Onthe other hand, the metal surface of the sidewall 127 and of theconductive face of the pad 120 cause an X-signal which is substantiallylarger than the R-signal of interest and larger than the X-signalencountered without conductive bodies in proximity to the antenna set69. Because of the degree and stability of the electromagnetic symmetrywhich the present invention achieves, however, the very large X-signalcancels and the high resolution is realized.

The important parameter in resolution enhancement has been found to bethe length of the aperture in the direction parallel to the motion ofthe pad 120. Improved resolution is achieved with shorter longitudinalaperture length.

The theory explaining the focussing is readily appreciated on anintuitive level. High frequency magnetic fields are excluded from theinterior of metal due to skin effect. The metal backplane 127 and metalsidewall 127, for instance, excludes the high frequency magnetic fieldfrom the metal body 122 and confines the field tightly within thecavity. Moreover, the high frequency magnetic field also tends to beconstrained outside of the cavity, parallel to the sidewall of thecylindrical cavity, due to a boundary condition imposed on the magneticfield.

The elements of antenna set 69 are fabricated from suitable materialsand assembled into a unitary package suitable for use in the boreholeenvironment. While the general symmetry of the sensor 70 makes itlargely self-compensating with respect to thermal expansion and pressureinduced compression and hence scale invariant, better performance of thesensor 70 is achieved by ensuring essentially stable dimensions. Hence,components that strongly influence dimensional stability are made frommaterials having low thermal expansion coefficients and lowcompressibilities. The nonconductive materials preferably have a lowdielectric loss as well. For example, in fabricating the transmitterloop 10, receiver loops 12 and 14, and the individual shield elements, aceramic substrate material preferably is used. Moreover, the variousceramic substrates of the antenna set 69 may advantageously serve asspacing elements by proper selection of substrate thickness.

The assembled antenna set 69 having a wall-engaging face 112 and anopposing face 114 and comprising substrates 86, 88, 90, 92, 94, and 96is shown in FIG. 6. Each of the substrates measure about 4.4 cm indiameter. The transmitter loop 10 lies approximately in the centralplane of antenna set 69, between thin substrates 90 and 92, and isconnected to lead 100. The 0.69 cm spacing between the transmitter loop10 and receiver loop 12 is obtained with stacked substrates 90 and 88,which measure approximately 1.5 mm and 0.675 cm respectively. A shieldelement such as shown at 80 in FIG. 5, but measuring only about 4.4 cmin diameter and hence having only 128 segments, lies between thesubstrates 90 and 88, coaxial with transmitter loop 10. Theapproximately 0.68 cm spacing between the transmitter loop 10 andreceiver loop 14 is obtained with stacked substrates 92 and 94, whichmeasure approximately 1.5 mm and 0.665 cm respectively. A shield elementsuch as shown at 80 in FIG. 5, but measuring only about 4.4 cm indiameter and hence having only 128 segments, lies between the substrates92 and 94, coaxial with transmitter loop 10. Two additional shieldelements such as shown in FIG. 5, but meauring only about 4.4 cm indiameter and hence having only 128 segments, are provided respectivelybetween the receiver loops 12 and 14 and the external environment. Theseshield elements are coaxial with the receiver loops 12 and 14 spacedfrom the receiver loops 12 and 14 respectively by the thickness ofsubstrates 86 and 96, each of which measures about 1.5 mm. It will beappreciated that these dimensions are illustrative.

A screw (not shown) capable of being moved along the axis of and intothe antenna set 69 may be provided to fine tune the cancelation of thedirect mutual coupling. In the event that a tuning screw is used, theconductive center of a shield element such as 80 through which the screwmay pass must be enlarged to accommodate an orifice for the tuningscrew. The resulting ring-like conductive center should be opened alonga ray to prevent induction of eddy currents.

The shield element provided at the face 114 between receiver loop 14 andthe environment external to it, which is the backplane 126 as shown inFIG. 7, is fabricated on substrate 96 as described above. The shieldelement provided at the face 112 between receiver loop 12 and theenvironment external to it, which is the formation being investigated,performs the additional function of protecting the antenna set 69 fromthe abrasive action of the wall of borehole 30. Hence, this shieldelement preferably is machined from a block of suitable conductivematerial such as brass or stainless steel.

A transmitter loop, receiver loop, or shield element of the antenna set69 may be fabricated on either adjoining face of the substrates betweenwhich it lies. For example, transmitter loop 10 may be fabricated on theface of substrate 92 nearest face 112, or on the face of substrate 90nearest face 114. The various substrates are bonded to one another alongrespective adjoining faces by means of a suitable bonding adhesive. Caremust be taken in assembling the antenna set 69 to avoid imperfections inconstruction that might lead to residual direct mutual coupling betweenthe transmitter loop 10 and receiver loops 12 and 14. The receiver loops12 and 14 and the shield elements must be coaxial with respect to thetransmitter loop 10. All elements thereof, including the ceramicsubstrates and unshielded leads, as well as any fasteners that might beused, must be symmetrically located insofar as possible, with theexception noted above.

In pad 120, respective conductors 128 and 129 connect the transmitterloop 10 and the receiver loops 12 and 14 to respect networks 130 and132, the purposes for which are explained below. Network 130 is coupledto transmitter circuitry in the sonde body by cable 134, and network 132is connected to receiver circuitry in the sonde body by cable 136.Cables 134 and 136 may be of a flexible coaxial type. Ferrite beadsselected to have a large dissipation factor in the frequency range ofinterest are used on unshielded low-frequency leads and on the outerconductor of coaxial cables to reduce radio frequency currents on these

Other pad arrangements are possible. For example, where the focussingand isolating functions performed by the metalization of the antenna set69 or by the cavity in the pad body 122 are not desired, the pad bodymay comprise mostly dielectric material and a sensor such as sensor 7may be mounted therein. Variations of the antenna set 69 arecontemplated as well. For example, while reduction of thetransmitter-receiver loop spacing generally reduces output signallevels, the transmitter-receiver loop spacing can be reduced by morethan a factor of two without significant deterioration of performance.Moreover, a shield of reduced area also can be effective.

An electrical circuit suitable for operating the sensor 70 is shown inFIG. 8. The pad 54(1) includes transmitter loop 10 and receiver loops 12and 14, which are operated like a dual-secondary mutual inductance coilset. The transmitter loop 10 and receiver loops 12 and 14 are coupled totransmitter section 141 and receiver section 143 respectively throughnetworks 130 and 132, which preferably are tuned to their respectiveloop antennas. The networks 130 and 132 are mounted on the pad 54(1)preferably in proximity to transmitter loop 10 and receiver loops 12 and14 respectively, as variations in the electrical properties of wiringbetween a loop antenna and its respective network will adverselyinfluence the tuning. Network 130 is constructed so that the transmitterloop 10 is driven in a balanced mode, to reduce the monopole componentof the electric field. Network 130 minimizes reflections from thetransmitter loop 10, which typically has a real impedance of less thanan ohm. Receiver loops 12 and 14 are connected in series oppositionthrough network 132, which is a subtractive network such as a balun,four port hybrid junction, or differential amplifier, that enables thedirect mutual inductance to be nulled. A calibration switch 138 isconnected across the leads from the receiving loop 14. The function ofthe calibration switch 138 is described below.

A sensor circuit 140(1), which comprises the transmitter section 141 andthe receiver section 143, is located in the body of the tool 51. Thetransmitter section 141 comprises a continuous wave source oscillator142 operating at a desired radio frequency. The output of oscillator 142is supplied via directional coupler 144 to an amplifier 146, where thesource energy is amplified and applied to transmitter loop 10 throughthe network 130. The source energy is split at the directional coupler144, and supplied as a reference signal to the reference channel of aphase sensitive detector 148 in the receiver section 143. The phasesensitive detector 148 also is supplied at its signal channel with thesignal from the receiver loops 12 and 14, applied through amplifier 149.Phase sensitive detector 148 provides at its output signal indicative ofthe power ratio and phase shift of the signal received at the receiverloops 12 and 14. Good isolation of the transmitter section 141 and thereceiver section 143 is necessary since the sensor 70 has an insertionloss of -120 dB or more in the absence of a conductive formation.

Essentially identical sensor circuits 140(2), 140(3), and 140(4) arerespectively connected to pads 54(2), 54(3), and 54(4). The power ratioand phase shift signals from the sensor circuits 140(1), 140(2), 140(3),and 140(4) are supplied to the input of a multiplexer 150, where theyare sampled and supplied to an A/D converter 152. The output of the A/Dconverter 152 is supplied to the input of a telemetry system 154 fortransmission to the surface equipment, which includes the processor 25.

The formation signal detected by, for example, the laboratory sensorcomprised two components, one influenced principally by the conductivityof the formation and another influenced principally by the dielectricconstant of the formation. The conductivity influenced component(R-signal) is preferred for use in the dip determination rather than thedielectric constant influenced component (X-signal) since contrasts information dielectric constant are generally smaller than contrasts inconductivity. The R-signal is coupled into the receivers in phase withthe driving signal. All other signals, generally grouped as "nuisance"signals and including the X-signal, signals attributable to anyunbalanced direct mutual inductance, and signals attributable to metals,are coupled into the receiver circuits 90° out of phase with the drivingsignal.

Phase sensitive detection may be advantageously used to reject all ofthe unwanted coherent signals, as well as incoherent noise. The phasesensitive detector 148 must be calibrated periodically, however, becausecables, transformers, amplifiers and other such components contribute tophase shifts within the sensor circuit. Since the direct mutualinductance is 90° out of phase with the driving signal, a very largequadrature signal can be generated merely by shorting one of thereceiver loops 12 and 14. A calibration switch 138 (FIG. 8) is providedfor this purpose. The angle so measured then is subtracted from 90°, andthe resultant calibration angle is stored by processor 25 so thatformation phase measurements may be adjusted for these miscellaneousphase shifts. To determine a parameter that is proportional toconductivity, the measured amplitude is multiplied by the cosine of theadjusted phase measurement in processor 25. All nuisance effects arerejected in the sine component.

The operation of the present invention will be understood by consideringexperimental results achieved with the experimental sensor describedabove. A laboratory formation was constructed comprising alternatinglayers of saline water and a synthetic, granular, porous materialsaturated with the saline water. The synthetic material was Kellundite(Trademark) FAO-100 manufactured by Ferro Corporation of Rochester, N.Y.The material resembles clean sandstone when viewed under a scanningelectron microscope. It has a porosity of about 40 percent, a formationfactor of 5.5, and a permeability of several Darcies. The sample wassaturated with water having a resistivity of 1 Ω-m, approximately theresistivity of shale. The circuit used in the laboratory experiments wassimilar to sensor circuit 140(1) and networks 130 and 132. Theoscillator and phase-sensitive detector were elements of aHewlett-Packard model 8505A network analyzer. A broadband amplifier witha gain of 33 dB fed the signal channel of the network analyzer, while a40 dB attenuated source signal fed the reference channel. The networkanalyzer was under the control of a Hewlett-Packard model 9845Bcomputer, which also governed the motions of the experimental mechanism.

The response of the laboratory sensor is readily appreciated on anintuitive level through a simple and approximate model known as "averageloop response." The "average loop" is taken as the single ground loopthat best approximates the average of the geometrical factor taken overall ground loop radii.

The response of the laboratory sensor to thin beds such as the shalestreak 44 in FIG. 2 was found to depend on whether the thin bed was moreresistive than the shoulders or more conductive. A thin resistive bedwas found to reduce eddy currents in the surrounding conductiveformation and to lead to a simple negative-going peak in the response,centered on the location of the resistive streak. This response, a"normal" response, is illustrated in FIG. 9. A thin resistive bed 158comprising an insulating sheet 0.64 cm thick lay between relativelyconductive beds 156(1) and 156(2). The resistive bed 158 was readilydetected, as indicated by the sharp negative-going peak of trace 157.The normal response pattern is illustrated for a layered sequence inFIG. 10. The layered sequence comprised resistive beds 160(1), 160(2),160(3), 160(4), and 160(5) and conductive beds 170(1), 170(2), 170(3),170(4), and 170(5) in an alternating sequence. Each resistive bed 160was 1.26 cm thick with resistivity 5.5 Ω-m. Each conductive bed 170 was3.81 cm thick with resistivity 1.0 Ω-m, the thickness of the conductivebeds 170 being as large as or larger than the diameter of the averageloop. The response of the laboratory sensor, which is shown as trace180, to the conductive beds 170 was a sequence of single positive-goingpeaks, while the response of the laboratory sensor to the thin resistivebeds 160 was a sequence of single negative-going peaks.

The response of the laboratory sensor to a conductive streak is somewhatcomplex. Following from the average loop concept, the response of thelaboratory sensor is roughly proportional to the arc length of theaverage loop that falls within the thin conductive bed as the averageloop passes over. The length of the arc is a maximum when the edge ofthe average loop intersects the thin bed, and is a local minimum whenthe sensor is centered on the thin bed. Essentially, the thin bed isbeing picked up by the "horns" of the geometrical factor. This"inverted" response is illustrated in FIG. 11, which shows a 0.64 cmthick 1 Ω-m layer imbedded in a uniform 5.5 Ω-m formation 190. Thesignal level as represented by curve 185 increased as the laboratorysensor approached the thin conductive bed 180, dropped sharply as thelaboratory sensor moved directly over the thin conductive bed 180,increased as the laboratory sensor moved away from the thin conductivebed 180, and finally fell off as the laboratory sensor moved completelyaway from the thin conductive bed 180. The asymmetry and noise on thecurve 185 are due to limitations in the laboratory model and equipment.

The central dip found when scanning a single thin conductive bed such asbed 180 in FIG. 11 is manifested for a formation containing many suchbeds as an inversion of the signal. This is illustrated in FIG. 12,which shows a 10 cm thick resistive bed 200 followed by alternating thinconductive beds 202 and comparatively thick resistive beds 204. The thinconductive beds 202 are 0.63 cm thick with 1 Ω-m resistivity. Thecomparatively thick resistive beds 204 were 1.27 cm thick with 5.5 Ω-mresistivity. Coming off of the thick resistive bed 200, the trend in theresponse curve 210 is positive, as would be expected. In the finelylaminated region comprising alternating beds 202 and 204, the largersignal is associated with the resistive regions 204. This is the"inverted" response. The response of the laboratory sensor shown bycurve 210 in FIG. 12 is to be contrasted with the "normal" response 180shown in FIG. 10. Conductive beds smaller than about 2.5 cm result ininverted behavior, while larger beds do not.

Although the thickness of the conductive beds under investigation doesinfluence whether a response will be normal or inverted, the effect doesnot interfere with the calculation of dip. An essential characteristicof a dipmeter is that it produces signals that are correlatable amongthe several pads. This condition is satisfied in the normal and invertedresponse patterns. Any suitable correlation technique, several of whichwere referenced above, may be advantageously used to determine dip.

Sensor 70 may be operated over a wide range of frequencies. The lowerfrequency limit at which sufficient signal strength is realized is about1 MHz, although other dimensions and parameters can be selected toreduce this lower limit. Regardless, high frequency operation ispreferred, since the formation signal voltage is proportional to thesquare of the frequency. Several factors limit the upper frequencyextent, however. A fundamental limit is set by the skin effect, whichconfines electromagnetic signals to within a finit skin depth of thesurface of a conductive body. The skin depth δ is given by ##EQU8## If δis measured in meters, then μ is the permeability in H/μ, f is thefrequency in Hz, and σ is the conductivity in mho/m. As long as the skindepth is larger than the spatial extent of the field produced by thetransmitter loop 10 and sensed by the receiver loops 12 and 14,resolution and depth of investigation of the sensor will be independentof formation conductivity. Such independence is desirable. Anotherlimitation is the self-resonance of the antennas and cabling. Theantenna loops used in the laboratory sensor have self-resonancefrequencies in the range of several hundred megahertz, although theattachment of relatively short cables reduces these frequencies toaround 90 MHz. At or above such a frequency, the sensor is insensitiveto formation properties. With adequate attention paid to cabling issues,it is reasonable to use frequencies of 100 MHz or more.

Some laboratory experiments were conducted at 12 MHz, 25 MHz, and 55 MHzto investigate sensor performance at different frequencies. As expected,the signal-to-noise ratio increased dramatically at the higherfrequencies. At 55 MHz, the skin depth in a 1 Ω-m formation was 6.8 cm,which is larger than the distance at which formation signals are sensed.

Sensor 70 should be capable of being operated at a power level in excessof 20 watts if ceramic technology appropriate to borehole applicationsis used. It was found that 20 watts of power could be delivered to thelaboratory sensor. The sensitivity of the laboratory sensor at low powerlevels was investigated. The receiver bandwidth was set at 10 kHz. Theformation was composed of alternating 1.27 cm layers of 5.5 Ω-mresistivity and 0.63 cm layers of 1.0 Ω-m resistivity. The 100 mWresults were essentially found to be free of noise, the 10 mW resultsevidenced a small amount of noise, and the 1 mW results evidencedsubstantial noise, although not enough to entirely obscure the layeringof the formation.

Receiver bandwidth and borehole logging speed were found to beinterrelated. Receiver bandwidth has a direct effect on signal-to-noiselevel, as thermal noise power is directly proportional to it. Thelaboratory instrumentation had selectable IF stage filter bandwidths of10 kHz and 1 kHz. A video (power averaging) filter was also availablewith a bandwidth of 30 Hz. Bandwidth limitation is beneficial inincreasing the signal-to-noise ratio. Nonetheless, the measurement mustbe sufficiently broadband to permit a reasonable logging speed. Considerthe case in which it is desirable to log at 1800 ft/hr and collect dataevery 0.2 inches. Then the receiver is being sampled 30 times persecond. Hence, the receiver bandwidth can be no less than about 30 Hz.Trade-offs among dynamic range, power consumption, logging speed, andsignal to noise ratio need to be considered in designing and operatingthe sensors of the present invention.

An embodiment of electromagnetically symmetrical sensor for absoluteformation measurements which does not depend on physical symmetry isillustrated in FIG. 13. The sensor includes an antenna set 669comprising form 602 and antennae 610, 612 and 614, mounted in acylindrical cavity provided in a nonconductive pad body 622. The axis ofthe antenna set 669 in FIG. 13 is normal to the face of the pad body622, although the antenna set 669 may be mounted with its axis parallelto the face of pad body 622 to achieve an absolute measurement as well.Mounting in a metal pad is possible, and would result in enhancedfocussing and improved reliability because of the influence of aconductive sidewall and backwall, substantially as previously discussed.

The ceramic form 602 functions as a substrate for the transmitter loopantenna 610, the receiver loop antenna 612, and the receiver loopsolenoid 614, which are fabricated on the form 602 using knownphotolithography technology. The respective central planes of theantennae 610, 612 and 614 preferably are common, although they may beoffset at the expense of increasing the thickness of the antenna set.The cavity in which antenna set 669 is mounted is suitably sealed (notshown) from the external environment at the face of the pad body 622.Suitable illustrative values for the parameters of antenna set 669 area=1 cm., b=2 cm., c=3 cm., and N_(a) /N_(b) =4.732.

The principle of operation essentially is as follows: If an antenna A(the inner solenoid 614) is considered to have "N_(a) " turns of radius"a," an antenna B (the middle antenna 612) is considered to have "N_(b)" turns (where N_(b) -1) of radius "b;" and an antenna C (the outerantenna 610) is considered to have "N_(c) " turns (where N_(c) -1) ofradius "c;" then the voltages V_(a) ⁰ and V_(b) ⁰ respectively inreceivers A and B from the mutual inductances M_(ac) and M_(bc) is

    V.sub.a.sup.0 =jωM.sub.ac I.sub.c                    (18)

    V.sub.b.sup.0 =jωM.sub.bc I.sub.c                    (19)

The radii and turn ratio N_(a) /N_(b) is selected to force M_(ac)=M_(bc) so that:

    V.sub.0 =V.sub.a.sup.0 -V.sub.b.sup.0 =+jω(M.sub.ac -M.sub.bc)I.sub.c =0                                                        (20)

With the direct mutual cancelled, the formation signal is readilyavailable. Consider an elemental ring in the formation of radius r, at adistance of z from a pad, with cross-sectional area ΔrΔz. The voltageinduced in this ring is:

    ΔV.sub.f =jωM.sub.fc I.sub.c                   (21)

where M_(fc) is the mutual inductance between the ring and antenna C.The eddy current in the ring is: ##EQU9## This induces a voltage inantenna A, given by: ##EQU10## where M_(af) is the mutual inductancebetween antenna A and the ring. In the manner, the signal in antenna Bis: ##EQU11## The total signal in the pair of receivers is given by thedifference voltage, integrated over the formation: ##EQU12## The term inthe brackets is the "geometrical factor", which multiplies the formationconductivity.

The antenna set 669 may be operated with the circuit of FIG. 8, forexample. Phase sensitive detection is used to improve thesignal-to-noise ratio. Since the measurement preferably is a shallow,high resolution measurement, high frequency operation may be used tofurther improve the signal-to-noise ratio, since the formation signal isproportional to ω², while the direct mutual signal is proportional to ω.

Other antenna in the antenna set 669 may be selected for operation astransmitter. For example, antenna 614 is to be selected where a deeperinvestigation is desired, although the vertical resolution would be madecorrespondingly greater. Suitable illustrative values for the parametersof such a sensor are a=1 cm., b=2 cm., c=3 cm., and N_(c) /N_(b) =1.596.

When oriented as shown in FIGS. 1 and 7, sensors such as 7 and 70provide an absolute measurement of formation conductivity. It has beenfound that an orientation of the transmitter loop 10 and receiver loops12 and 14 set at 90° from that maintained in sensor 7 provides adifferential measurement. A sensor 270 of this type, in whichtransmitter loop 10 and receiver loops 12 and 14 are rotated 90° in theradial plane of the borehole and hence "edgewise" to the wall of theborehole 30, is illustrated in FIG. 14. While the sensor 270 operates onthe same basic principle as the sensor 7, the interaction with theformations under investigation differs. FIG. 14 shows a formation 280such as, for example, a shale bed, lying between formations 275 and 290such as, for example, sand beds which meet one another along boundaries283 and 285 respectively. The transmitter loop 10 establishes a primarymagnetic field, represented in FIG. 14 by exemplary field lines B_(p).The primary magnetic field B_(p) establishes an electric field whichintersects the wall of the borehall 30, causing a charge accumulation tooccur thereon. The resulting average unit ground loop 287 in turninduces a secondary magnetic field B_(s), the field lines of which areintersected by the receiver loops 12 and 14.

FIG. 15 may be referred to for a qualitative understanding of theresponse of sensor 270 as it is drawn up borehole 30. The response ofthe sensor 270 to the homogeneous isotropic formation 290 is essentiallyflat (see curve section 308) until the sensor 270 draws near to theborder 285 between formation 290 and formation 280. As the sensor 270draws near to the formation 280, which is relatively impermeable to thenonconductive mud filtrate and hence is more conductive than formations275 and 290, the formation eddy currents shift preferentially toward themore conductive layer 280. In other words, the average unit ground loop14 shifts nearer to the plane of the receiver loop 14 than to the planeof the receiver loop 12. Hence, receiver loop 14 intersects more linesof the flux of the secondary magnetic field B_(s) than does receiverloop 12, resulting in the positive response peak (see curve section310). The differential measurement decreases as the transmitter loop 10moves into the conductive formation 280 until the differentialmeasurement once again is flat (see curve section 312). This sequence ofevents is reversed as the transmitter loop 10 moves toward the boundary283 between formation 280 and formation 275. The differentialmeasurement drops to a negative peak (see curve section 314) as thetransmitter loop 10 moves across the boundary 283. As the transmitterloop 10 moves well away from the boundary 283, the differentialmeasurement rises and then flattens out (see curve section 316).

FIG. 15 was produced in a laboratory experiment. The conductive layer280 was simulated by a salt water bath, while relatively nonconductiveformations 275 and 290 were simulated by air.

While a sensor such as 270 or antenna set 669 oriented with its axisparallel to formations traversed by the borehole are suitable for use ina borehole tool such as 51 having pads such as 54, the thickness of eachpad 54 must be sufficient to accomodate the diameter of the transmittingloop 10, receiver loops 12 and 14, and any shield elements such as mightbe desired. A preferred arrangement which makes possible a pad 54 havinga small thickness and providing better isolation for an antenna set isshown in FIG. 16, applied to an arrangement similar to sensor 270. Thesensor 370 is shown disposed in borehole 30 adjacent formation 300. Thissensor 370 comprises a backplane 302 and a transmitter half-loop 310.Two receiver half-loops 312 and 314 are located symmetrically about thetransmitter half-loop 310, coaxial therewith. The transmitter half-loop310 is connected to a source of oscillatory current 16 by leads 320 and321, which pass through backplane 302. The receiver half-loops 312 and314 are connected in series opposition by lead 323, and to a receiver 18by leads 322 and 324. Image currents arising in backplane 302 result insensor 370 performing essentially identically with sensor 270 of FIG.14.

An exemplary pad 400 which includes the sensor 370 is shown in FIG. 17.An antenna set 369, which includes transmitter half-loop 310 andreceiver half-loops 312 and 314 fabricated, for example, with theceramic technologies described above, is shown residing within arectangular cavity formed in the metal body 422 of the pad 400 andsecured with a suitable abrasive-resistant dielectric material 421. Theantenna set 369 preferably is centered in the cavity. The distancebetween the antenna set 369 and the cavity walls is selected on thebasis of the degree of focussing desired. The antenna set 369 is backedby a backplane section 302 of the metal body 422. Wires 428 and 429connect the transmitter half-loop 310 and the receiver half-loops 312and 314 to respective networks 430 and 432. The network 430 is coupledto the transmitter circuitry in the sonde body by cable 434, and thenetwork 432 is connected to receiver circuitry in the sonde body bycable 346. Cables 434 and 436 may be of the flexible coaxial type.Ferrite beads selected to have a large dissipation factor in thefrequency range of interest should be used on unshielded low-frequencyleads and on the outer conductor of the coaxial cables to reduce radiofrequency currents on the structures.

Suitable electrical circuits for the sensor 370 have been describedabove. The operation of sensor 370 also has been described above withrespect to FIG. 14. Since the output of the sensor 370 is correlatablewith the output of other similar sensors, any one of severalconventional dip determining techniques may be applied for determiningdip.

While the present invention has been described with reference to severalparticular embodiments, it is to be appreciated that the embodiments areillustrative only in that the invention is not intended to be limited toonly the disclosed embodiments. Variations and combinations within thespirit and scope of the invention will occur to those skilled in theart. One such variation, which is suitable for making a differentialmeasurement, is illustrated in FIGS. 18 and 19. The coplanar spacedtransmitter loops 501 and 503 of FIG. 18, or other suitable fieldgenerating means such as a single transmitter loop in the plane of loops501 and 503 but with its axis coincident with line a--a', are maintainedwith their axes normal to the surface of the formation 510 underinvestigation. Transmitter loops 501 and 503 are coupled to a source 505or oscillatory current so as to generate respectively opposed primarymagnetic fields, represented by an exemplary field line B_(p). Thecomposite primary magnetic field induces eddy currents in formation 510that are greatest in the place defined by the locus equidistant from theaxes of the transmitter loops 501 and 503 and represented in FIG. 17 byline a--a'. Coplanar receiver loops 507 and 509, mounted in mirror imageabout the plane represented by line a--a' and preferably mountedcoaxially with transmitter loops 501 and 503 as shown, intercept thelines of flux of a secondary magnetic field arising from the inducededdy currents. Receiver loops 507 and 509, which are connected in seriesopposition to a receiver 511, are electromagnetically symmetrical. Theresponses of the receiver loops 507 and 509 to both the primary andsecondary magnetic fields cancel in a homogeneous isotropic formation;in the vicinity of a shoulder, for example, only their responses to theprimary magnetic field cancel. A variation of the sensor of FIG. 18 isshown in FIG. 19, where the transmitting antenna loop 510 and thereceiver antenna loops 512 and 514 lie in a common plane. Of course, thephotolithography and assembly techniques discussed above areadvantageous for the sensors of FIGS. 18 and 19 as well. Accordingly,variation in these and other features are contemplated and are withinthe scope of the present invention. Moreover, it will be appreciatedthat sensors equivalent to those described herein may be obtained byinterchanging the functions of the transmitter antennae and the receiverantennae. Hence, electromagnetic symmetry of transmitter antennae aswell as of receiver antennae is contemplated. It will be understood thatalthough the preferred orientation of the axes of theelectromagnetically symmetrical antennae to the other antenna orantennae of each of the several embodiments is described herein asnormal or parallel, as the case may be, electromagnetic symmetry can beachieved in these embodiments in accordance with the spirit of thepresent invention with intermediate orientations as well.

What is claimed is:
 1. An apparatus for investigating a characteristicof earth formations traversed by a borehole, comprising:a body having aface opposing the borehole wall; means for moving said body in theborehole; a first antenna element mounted in said body and comprising aconductive member conformably mounted on a stable form member; a secondantenna element mounted in said body and comprising a conductive memberconformably mounted on a stable form member; and a third antenna elementmounted in said body, said third antenna element being essentiallyidentical to said second antenna element; wherein said first, second andthird antenna elements are scale invariant relative to one another andintegrally assembled; and wherein the respective locations andorientations of said second and third antenna elements are selected toplace said second and third antenna elements in electromagnetic symmetryabout said first antenna element; and means for differentially couplingsaid second and third antenna elements.
 2. An apparatus as in claim 1,wherein the plane of symmetry of said second and third antenna elementsis oriented normal to the wall-engaging face of said body for obtaininga differential measurement of said characteristic.
 3. An apparatus as inclaim 2, wherein said body comprises a conductive backplane memberoriented parallel to the wall-engaging face thereof, said first, secondand third antenna elements being located between said backplane memberand the wall-engaging face of said body.
 4. An apparatus as in claim 1,wherein the plane of symmetry of said second and third antenna elementsis oriented parallel to the wall-engaging face of said body forobtaining an absolute measurement of said characteristic.
 5. Anapparatus as in claim 4 wherein said body comprises a conductivebackplane member oriented parallel to the wall-engaging face thereof,said first, second and third antenna elements being located between saidbackplane member and the wall-engaging face of said body.
 6. Anapparatus as in claim 1, wherein:said first antenna element comprises aconductive loop of a selected diameter photolithographically fabricatedon a ceramic substrate; said second antenna element comprises aconductive loop of a selected diameter photolithographically fabricatedon a ceramic substrate; and said third antenna element comprises aconductive loop of a diameter equal to the diameter of the conductiveloop of said second antenna element, photolithographically fabricated ona ceramic substrate.
 7. An apparatus as in claim 1, wherein said first,second and third antenna elements are coaxial loop antenna, and whereinthe loop antennae of said second and third antenna elements are locatedessentially symmetrically about the antenna loop of said first antennaelement.
 8. An apparatus as in claim 1, wherein said first, second andthird antenna elements are coplanar loop antennae, and wherein the loopantennae of said second and third antenna elements are locatedessentially symmetrically about the antenna loop of said first antennaelement.
 9. An apparatus as in claim 1, wherein each of the conductivemembers of said first, second and third antenna elements comprises aloop of highly conductive material.
 10. An apparatus as in claim 9wherein said second and third antenna elements are positioned coaxialand parallel to said first antenna element and essentially equidistantthereto.
 11. An apparatus as in claim 9, wherein said body furtherincludes means for shielding against electroquasistatic coupling betweenthe first, second and third antena elements, respectively.
 12. Awall-engaging apparatus for investigating a characteristic of earthformations traversed by a borehole, comprising:a body having a boreholewall engaging face and a conductive backplane; means for moving saidbody in the borehole; an antenna set mounted in said body between saidface and said backplane, including first, second and third antennaelements, said second and third antenna elements being identical to eachother and being positioned in electromagnetic symmetry about said firstantenna element; means for differentially coupling said second and thirdantenna elements; means for energizing a selected one of said firstantenna element and said differentially-coupled second and third antennaelements within a frequency range of 1 MHz and 300 MHz, to coupleelectromagnetic energy into a formation; and means coupled to the otherone of said first antenna element and said differentially-coupled secondand third antenna elements for receiving signals indicative of saidcharacteristic.
 13. An apparatus as in claim 12, wherein the plane ofsymmetry of said second and third antenna elements is oriented normal tothe wall-engaging face of said body for obtaining a differentialmeasurement of said characteristic.
 14. An apparatus as in claim 13,wherein said body comprises a conductive backplane member orientedparallel to the wall-engaging face thereof, said first, second and thirdantenna elements being located between said backplane member and thewall-engaging face of said body.
 15. An apparatus as in claim 12,wherein the plane of symmetry of said second and third antenna elementsis oriented parallel to the wall-engaging face of said body forobtaining an absolute measurement of said characteristic.
 16. Anapparatus as in claim 15, wherein said body comprises a conductivebackplane member oriented parallel to the wall-engaging face thereof,said first, second and third antenna elements being located between saidbackplane member and the wall-engaging face of said body.
 17. Anapparatus as in claim 12, wherein:said first antenna element comprises aconductive loop of a selected diameter photolithographically fabricatedon a ceramic substrate; said second antenna element comprises aconductive loop of a selected diameter photolithographically fabricatedon a ceramic substrate; and said third antenna element comprises aconductive loop of a diameter equal to the diameter of the conductiveloop of said second antenna element, photolithographically fabricated ona ceramic substrate; said first, second and third antenna elements beingintegrally assembled.
 18. A wall-engaging apparatus for investigating acharacteristic of earth formations traversed by a borehole, comprising:abody having a borehole wall engaging face and a conductive backplane;means for moving said body in the borehole; a transmitter antennamounted in said body between said face and said backplane for couplingelectromagnetic energy into a formation; a receiver antenna mounted insaid body between said face and said backplane and having differentiallycoupled identical antenna elements located in electromagnetic symmetryabout said transmitter antenna; means for energizing said transmitterantenna in the frequency range of 1 MHz and 300 MHz; and means coupledto said receiver antenna for obtaining an indication of saidcharacteristic.
 19. An apparatus as in claim 18, wherein the antennaeelements of said receiver antenna are coaxial and symmetrically locatedwithin the field pattern of said transmitter antenna.
 20. An apparatusas in claim 18, wherein the antennae elements of said receiver antennaare coplanar and symmetrically located within the field pattern of saidtransmitter antenna.
 21. A wall-engaging apparatus for investigating acharacteristic of earth formations traversed by a borehole, comprising:abody having a borehole wall engaging face and a conductive backplane;means for moving said body in the borehole; a receiver antenna mountedin said body between said face and said backplane; a transmitter antennamounted in said body between said face and said backplane and havingdifferentially coupled identical antenna elements located inelectromagnetic symmetry about said receiver antenna, for couplingelectromagnetic energy into a formation; means for energizing saidtransmitter antenna in the frequency range of 1 MHz and 300 MHz; andmeans coupled to said receiver antenna for obtaining an indication ofsaid characteristic.
 22. An apparatus as in claim 21, wherein theantennae elements of said transmitter antenna are coaxial, and saidreceiver antenna is located within the plane of symmetry of the fieldpattern of said transmitter antenna.
 23. An apparatus as in claim 21,wherein the antennae elements of said transmitter antenna are coplanar,and said receiver antenna is located within the plane of symmetry of thefield pattern of said transmitter antenna.
 24. A wall-engaging apparatusfor microinductively investigating a characteristic of earth formationstraversed by a borehole, comprising:a longitudinally elongatedconductive body adapted for a sliding engagement with the wall of saidborehole, said body having a wall-engaging face; a transmitter antennamounted in said body within a volume bounded in part by an integralconductive backplane and conductive sidewall and opening to thewall-engaging face of said body, for coupling focussed electromagneticenergy into a formation engaged by the wall-engaging face of said body;means for energizing said transmitter antenna; and means for detecting amagnetic field from said engaged formation arising from the coupledelectromagnetic energy.
 25. An apparatus as in claim 24, wherein saiddetecting means comprises a receiver antenna, said receiver antennabeing integrated with said transmitter antenna and mounted therewith insaid volume, said volume being conformal with said integratedtransmitter and receiver antennae.
 26. An apparatus as in claim 25,wherein said backplane is oriented parallel to the wall-engaging face ofsaid body, said transmitter and receiver antenna being located betweensaid backplane and the wall-engaging face of said body.
 27. An apparatusfor investigating a characteristic of earth formations traversed by aborehole, comprising:a body having a face opposing the borehole wall;means for moving said body in the borehole; an integrally assembledantenna set, mounted in said body, having at least one stable formmember, and first, second and third antenna elements which compriserespective first, second and third conductive members conformablymounted on said stable form member, said antenna elements being scaleinvariant relative to one another; said second and third antennaelements having respective locations and orientations being selected toplace them in electromagnetic symmetry about said first antenna element;and means for differentially coupling said second and third antennaelements.
 28. An apparatus as defined in claim 27 wherein said bodycomprises a conductive backplane member oriented parallel to said face,with said antenna set positioned between the backplane and the face. 29.An apparatus as defined in claim 28 wherein each of said conductivemembers comprises a conductive loop parallel to the conductivebackplane.